I posted a little link on the Origami Forum, located here: http://www.thekhans.me.uk/phpBB2 (there was a LOT more link there I trimmed out!) I came across this web forum of origami people! including quite a few people I know, like Gila, John McKeever, Boaz Shuval, etc. (I suppose “know” is being used here in a very casual way!) I’m hoping that I can have some interesting conversations on there. I hope I can wrangle Owesen to sign up if he ever shows up again around these parts.
http://en.wikipedia.org/wiki/Wallpaper_group this covers every regular and semiregular tessellation that we can fold, I think. or all the possible orientations. I haven’t thought through all the ramifications of this, but I’m pretty sure that anything that we can fold fits one of these models. things get a little more complicated topologically since the paper isn’t really “flat”, and there’s more dimensions to the folding, but that’s rather beyond me.
I found this through my technorati RSS feed for “tessellations”; it’s “Makoto Nakamura’s Tessellation World”. it has some really neat animated tessellation scenes, and some rather unique ideas. definitely worth a look. it’s all in Flash, so be forwarned if you are flash-free.
Christiane has a really slick new triangular tessellation online, as well as some great star models based on one of owesen’s puffy star shapes. check it out!
simple escher-style fish tessellation, v. 2 (backlit) Originally uploaded by Origomi. decided to try an escher-style tessellation again after some discussion on the Origami mailing list. this is, obviously, a rather simple model, but something more complex would take more time than I have right now. this model tessellates across the plane, although it requires two differently sized triangles to fill in some gaps. you can see the tiling pattern here. I know they don’t really look all that much like fish (more like goldfish crackers, if you’re from the US) but it’s what came to mind. I came up with some more complex figures made up of larger groups of shapes; I’ll try to give some of those a go at a later point in time. All my diagrams that exist are available online at: www.origamitessellations.com. I only have 4 documents up there currently, but there are more in the works. If I come up with some better fish tessellations I’ll make sure to diagram them!